The presence of \(B\)  in the Jacobian in an explicit form is very convenient. The magnetic field is weakly quasisymmetric iff the magnetic field magnitude is of the form \(B=B(\psi ,\chi )\) .[1]}, [2]} Thus, QS can be imposed by requiring the Jacobian to have the appropriate dependence only on the angular coordinate \(\chi \) . In this context, the integer \(N\)  determines the class of symmetry we are dealing with: \(N=0\)  for quasi-axisymmetry, and otherwise for quasi-helical symmetry. In this formulation, \(B\)  naturally appears as an input to the problem. Cast in this form, the formulation generalizes the classical form[3]}, [1]} and is less constraining than its strong form[5]}, [6]}, [2]}. It is also convenient to write the magnetic field in its covariant form,
\(\mathbf {B}=B_\theta \nabla \chi +(B_\alpha (\psi )-\bar{\iota }B_\theta )\nabla \phi +B_\psi \nabla \psi . \) 
